Discrete‐time repetitive controller for time‐delay systems with disturbance observer

A novel discrete-time repetitive controller design for time-delay systems subject to a periodic reference and exogenous periodic disturbances is presented. The main idea behind the proposed approach is to take advantage of the plant delay in the controller design, and not to compensate for the effect of this delay. To facilitate this concept, we introduce an appropriate time-delay and a compensator in a positive feedback connection with the plant, such that a generator for periodic signals is constructed. Then a proportional controller is used to stabilize the closed-loop system. The tracking control capability is thus guaranteed according to the internal model principle (IMP). In addition, to attenuate external periodic disturbances, a disturbance observer (DO) is developed to simultaneously achieve reference tracking and disturbance rejection. The possible fractional delay due to the digital discretization is handled by using a fractional delay filter approximation. The proposed controller has a simple structure, in which only a proportional parameter and a low-pass filter are required to be chosen. The closed-loop stability conditions and a robustness analysis under model uncertainties are studied. Numerical simulations and practical experiments on a servo motor system are conducted to verify the feasibility and simplicity of the proposed controller.